Sound wave behavior
Once a sound is introduced into a space, it is interrupted by objects, people, and boundaries of the space itself. Materials are varying degrees of two types: those that allow sound waves to pass through, and those that do not. When encountering barriers, sound waves are likely to behave in the following ways: absorption, transmission, refraction, reflection, diffusion, and diffraction.
Absorption occurs when a sound wave hits an obstacle and some sound energy is lost through its transfer to the molecules of the barrier; this energy is said to be absorbed. Thickness, porosity, frequency, and amplitude affect amount of absorption from a sound incident striking a surface.
Although some sound energy is lost molecularly in the composition of the obstruction, some will make it through and be audible on the other side. This is transmission, or a sound being able to transfer through an obstruction. When specifiers and designers are looking at sound privacy of one space to another, they are trying to control transmission.
Refraction is a variation of transmission. The difference is the soundwave bends as it passes through the obstruction.
The sound not absorbed or transferred through an obstruction often bounces back into a space. This phenomenon is called sound reflection, and is what specifiers and designers try to control in large, untreated echoic spaces.
A sound incident ray will often mirror off a flat hard surface, but additional rays can splay out from the incident ray. This is a process known as diffusion, the scattering of reflected sound rays.
Diffraction is also splaying of rays, but due to indirect impact. It is a product of sound moving around an obstruction and rays splintering, or diffracting, due to this physical relationship.
Additionally, sound produced in a space will bounce off reflective surfaces, gradually losing energy. When these reflections are mixed with each other, this is known as reverberation. Too much reverberation has a negative impact on speech intelligibility, and too little reduces the rich warm sounds like those from live music in an orchestra or concert hall setting.
Utilizing Sabine’s formula
Sabine’s formula measured the time it takes for sound energy to decrease by 60 dB after the sound incident has ceased. Measured in seconds, this is the reverberation time 60 dB (RT60). The rate of decay is going to depend on the amount of absorption in a room, its geometry, obstacles, and the properties of the sound incident itself; it will vary from space to space.
The RT60 is calculated by getting the volume of the space, and the amount of surface area (i.e. walls, floor, and ceiling). An absorption or attenuation coefficient is placed on each surface. As specifiers and designers know, most building materials are more reflective and less absorptive. The RT60 is 0.16 m (0.05 ft) times the volume of the space over the surface areas and individual coefficients. This number will reflect the time in seconds it will take a sound incident in this space to drop 60 dB.
The algebraic relationship of Sabine’s equation means any variable can be determined if the remaining components are known. Working the formula forward one can determine a modeled RT60 by knowing the volume, surface areas, and associated coefficient. Conversely, knowing the volume, the desired RT60, and the surface areas, one can determine how much treatment or absorptive coefficient material will be needed to achieve the desired effect or RT60.
For example, in a lecture hall with a desired two-second RT60, the calculation can be used to find a measurement of sabins (a sabin is one square foot of perfectly absorptive material). If 2100 sabins are needed, and a 50 percent absorptive material is being used, the amount of sabins are divided by the absorption coefficient, in this case 0.5, to come up with 390 m2 (4200 sf) of treatment needed to achieve the desired two-second RT60.
For general purposes, an RT60 of 1.5 to 2.5 seconds is considered acceptable for most spaces. Under the 1.5 second mark, there is a clearer articulation of speech, but the space starts to become acoustically dead, making it difficult to hear at the rear of the space, resulting in a loss of deeper bass tones. Above 2.5 seconds RT60, the space gains fullness and richness of sound but speech intelligibility suffers, and discerning words become difficult. Luckily, algebraic prowess is no longer a necessity for running these calculations, as several free, online acoustic reverberation calculators are readily available. These calculators can work forward to determine a space’s RT60, or backward to determine the amount of sabins or absorption needed to reach a desired RT60.